Question

A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find the probability that:

1. it bears a 2-digit number. 
2. the number is a perfect square.

Answer 1

In a box,

Total discs = 120

Sample space = {1, 2, 3, ...., 120}

i. Two-digit numbers = {10, 11, 12, 13,........., 99} = 90

P(bears a 2-digit number) = `90/120`

= `3/4`

ii. Number is a perfect square = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} = 10

P(number is a perfect square) = `10/120`

= `1/12`